A087649 a(n) = (1/2)*(Bell(n+2)-Bell(n+1)+Bell(n)).

1, 2, 6, 21, 83, 363, 1733, 8942, 49484, 291871, 1825501, 12054705, 83734241, 609851830, 4644041462, 36883843101, 304846039251, 2616765134351, 23286746418237, 214489200063218, 2041785040262972, 20060079966396887, 203156789589084133, 2118391734395139205

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Reinis Cirpons, James East, and James D. Mitchell, Transformation representations of diagram monoids, arXiv:2411.14693 [math.RA], 2024. See pp. 3, 33.

Formula

G.f.: (1-x+x^2)/(2*x*Q(0)) - 1/(2*x) + 1/2, where Q(k)= 1 - x - x/(1 - x*(2*k+1)/(1 - x - x/(1 - x*(2*k+2)/Q(k+1)))); (continued fraction). - Sergei N. Gladkovskii, May 13 2013

E.g.f.: exp(exp(x) - 1) * (exp(2*x) + 1) / 2. - Ilya Gutkovskiy, Aug 09 2021

Prog

(Magma) [(1/2)*(Bell(n+2)-Bell(n+1)+Bell(n)): n in [0..30]]; // Vincenzo Librandi, Nov 13 2011

Crossrefs

Cf. A000110, A035098, A059606.

Sequence in context: A058866 A063689 A178325 * A328435 A150222 A150223

Adjacent sequences: A087646 A087647 A087648 * A087650 A087651 A087652

Keyword

nonn

Author

Vladeta Jovovic, Sep 23 2003

Status

approved